# A three-dimensional Hellinger-Reissner Virtual Element Method for linear elasticity problems

## TL;DR

This paper introduces a 3D Virtual Element Method for linear elasticity problems using the Hellinger-Reissner principle, ensuring symmetric stresses and continuous tractions, with proven convergence and stability.

## Contribution

It develops a low-order 3D Virtual Element Method based on the Hellinger-Reissner principle, with theoretical analysis and numerical validation.

## Key findings

- Method achieves convergence and stability.
- Numerical tests confirm theoretical predictions.
- Ensures symmetric stresses and continuous tractions.

## Abstract

We present a Virtual Element Method for the 3D linear elasticity problems, based on Hellinger-Reissner variational principle. In the framework of the small strain theory, we propose a low-order scheme with a-priori symmetric stresses and continuous tractions across element interfaces. A convergence and stability analysis is developed and we confirm the theoretical predictions via some numerical tests.